List of vertices at intersection of two objects
Just a possible way to do this (there might be a better method to do this):

First set up materials on both objects (as in my answer in the link) and apply the boolean modifier: How to colour an indent that&#39;s been produced by a Boolean modifyer in 2.8

Then select by each individual materials, loop through them and save those vertices that are in common for both material selections. These should be the vertices you are looking for!

Happy blending!